Integer programming method for geographically distributing
identical resources

ABSTRACT

A METHOD FOR CONTROLLING A PROGRAMMABLE DIGITAL COMPUTER TO OPTIMIZE THE GEOGRAPHICAL DISTRIBUTION OF IDENTICAL RESOURCES WITH RESPECT TO A PLURALITY OF GEOGRAPHICALLY SEPARATED USES GIVEN THE COSTS ASSOCIATED WITH STORING SAID RESOURCE WHEN LOCATED AT EACH POSSIBLE LOCATION AND   THE COSTS ASSOCIATED WITH EACH USER COMMUNICATING WITH EACH POSSIBLE LOCATION.

DEFENSIVE PUBLICATION UNITED STATES PATENT OFFICE Published at the request of the applicant or owner in accordance with the Notice or Dec. 16, 1969, 869 0.6:. 687. The abstracts of Defensive Publication applications are identified by distinctly numbered series and are arranged chronologically. Ihe heading oi! each abstract indicates the number or pages of specification, including claims and sheets of drawings contained in the application as originally flied. The flies of these applications are available to the public for inspection and reproduction may be purchased for 30 cents a sheet.

Defensive Publication applications have not been examined as to the merits of alleged invention. The Patent Oflice makes no assertion as to the novelty oi the disclosed subject matter.

PUBLISHED APRIL 16, 1974 T921,022 INTEGER PROGRAMMING METHOD FOR GEO- GRAPHICALLY DISTRIBUTING IDENTICAL RESOURCES Richard George Casey, San Jose, Calif., assignor to International Business Machines Corporation, Armonk, N.Y.

Continuation of application Ser. No. 292,007, Sept. 25, 1972. This application Aug. 17, 1973, Ser. No. 389,395 Int. Cl. G06f 9/12 US. Cl. 444-1 4 Sheets Drawing. 33 Pages Specification A method for controlling a programmable digital computer to optimize the geographical distribution of identical resources with respect to a plurality of geographically separated users given the costs associated with storing said resource when located at each possible location and the costs associated with each user communicating with each possible location.

April 16, R G CASEY INTEGER PROGRAMMING METHD I OR GEOGRAPHICALLY DISTRIBUTING IDENTICAL RESOURCES Original Filed Sept. 25, 1972 v 4 Shoots-Shaet 1 R. G. CASEY TH April 16, 1974 RAPHICALLY DISTRIBUTING RCES GE E INTEGER PROGRAMMIN OD F TICA G ME IDE' 2 4 Shoots-Shoot 2-1 Original Filed Sept. 25, 197

April 16, 1974 R, CASEY TQZLOZZ INTEGER PROGRAMMING METHOD FOR GEOGRAPHICALLY DISTRIBUTING IDENTICAL RESOURCES Original Filed Sept. 25, 1972 4 Sheets-Sheet 1 INITIALIZE AND START ESTABLISH MIII IIx 0F VALUES K =(A *I )-A ESTABLISH MATRIX 0F VALUES II III-I Q' II I 'A {u la eK /\0(o C(u -(1Z)) l COMPUTE VALUE I2=I,2,---,n m

cIII =Z U +Z 6 (1) kEI =I WHERE (I) Is THE IIIIIEx sEI if()( CONTAINING ALL n POSSIBLE NODES COMPUTE VALUES N0 wIIEIIE III Is IIIE COLLECTION m =0 9 YES OPTIMUM 0F INDEX SETS CONTAINING ALL k ASSIGNMENT IS 0* EXCEPT THE irh NODE A =fi CONSTRUCT INDEX SET (1 CONTAINING I IosE k NODESI WHERE C(I) C(I) April 16, R, CASEY TQZLOZZ INTEGER PROGRAMMING METHOD FOR GLOGRAPHICALLY DISTRIBUTING IDENTTCAL RESOURCES Original Filed Sept. 25, 1972 4 Sheets-Sheet 4 STORE ELECTRICAL SIGNALS REPRESENTING QUERY AND UPDATE TRAFFIC FROM EACH POSSIBLE RESOURCE LOCATION, AND THE COMMUNICATION COSTS REPRESENT EACH POSSIBLE RESOURCE ALLOCATION AS A VERTEX ON COST GRAPH, SAID VERTICES BEING INTERCONNECTED BY PATHS REPRESENTING THE ADDITION OF A SINGLE RESOURCE TO THE PREVIOUS ALLOCATION CONTROL THE COMPUTER TO CALCULATE FROM SAID STORED SIGNALS THE COST ASSOCIATED WITH THE VERTEX REPRESENTING THE ALLOCATION OF A RESOURCE TO ALL POSSIBLE LOCATIONS 1 CONTROL THE COMPUTER TO CALCULATE THE COST ASSOCIATED WITH EACH VERTEX REPRESENTING THE ALLOCATION OF A RESOURCE TO ALL EXCEPT ONE POSSIBLE LOCATIONS STORE ELECTRICAL SIGNALS REPRESENTING THE BEGINNING VERTEX, SAID BEGINNING VERTEX REPRESENTING THE ALLOCATION OF RESOURCES TO THOSE SAID EXCEPT ONE POSSIBLE LOCATIONS WHERE THE COST ASSOCIATED WITH THE ALLOCATION OF A RESOURCE TO ALL EXCEPT ONE POSSIBLE LOCATION IS GREATER THAN THE COST ASSOCIATED WITH THE ALLOCATION OF A RESOURCE TO ALL POSSIBLE LOCATIONS STORE ELECTRICAL SIGNALS REPRESENTING THE MAXIMUM NUMBER OF PATHS TO BE TRACEDIN PARALLEL FROM ONE LEVEL OF THE COST GRAPH TO THE NEXT CONTROL THE COMPUTER TO TRACE PARALLEL PATHS FROM SAID BEGINNING VERTEX AND COMPUTE THE COST FUNCTION OF VERTICES ON SAID PATH UNTIL THE COST FUNCTION INCREASES, CLUSTERING THE PATHS SO THAT NO MORE THAN SAID MAXIMUM NUMBER IS TRACED FROM ONE LEVEL OF THE COST GRAPH TO THE NEXT STORE ELECTRICAL SIGNALS REPRESENTING THOSE VERTICES REPRESENTING AN ALLOCATION OF RESOURCES HAVING A LOCAL OPTIMUM COST FUNCTION WHEN THE COST FUNCTION HAS INCREASED ON EACH PATH BEING TRACED,

CONTROL THE COMPUTER TO SELECT FROM AMONG THE LOCAL OPTIMA ALLOCATIONS THE BEST ALLOCATION FIG.7 

